A Robust Well- Balanced Finite Volume Scheme for the OneDimensional Shallow Water

A Robust Well- Balanced Finite Volume Scheme for the One-Dimensional Shallow Water Equations

Abstract

The aim of this study was building a finite volume approach for numerically solving one-dimensional
shallow water equations, which applies to flat and non-flat terrain. The devised approach exhibits simplicity and
accuracy throughout the time integration process. The proposed methodology used a widely recognized HartenLax-Leer (HLL) solver for flux calculation. The suggested finite volume technique is a well-balanced,
conservative, non-oscillatory approach ideal for computing the flow depth in various flow regimes of shallow water
equations. The developed finite volume model dealt with the steady state of still water in a lake at rest. In addition,
the model was validated by applying it to several benchmark tests. The results showed a high concurrence with
analytical solutions based on the statistical tests. For the subcritical condition, the standard deviation was 5.73E-03,
the root mean square error was 5.84E-03, and the coefficient of determination was 0.9994. For the supercritical
condition, the standard deviation was 3.3E-02, the root mean square error was 3.334E-02, and the coefficient of
determination was 0.998.Furthermore, the suggested model effectively simulatesthe Hishkaro River's flow during
the flood season.